OVERVIEW

Two years ago, we ran a thematic program on o-minimality and real
analytic geometry. Its main focus was on extending local resolution
of singularities techniques in order to establish the o-minimality
of certain expansions of the real field, such as those generated by
the functions studied by Ilyashenko and Ecalle in his proof of Dulacs
problem. Many recent developments in the intersection of o-minimality
and real analytic geometry use resolution of singularities in crucial
ways, and they can in turn be viewed as extending the notion of resolution
of singularities in the sense of the preparation theorems mentioned
above. There is good reason to believe that extending resolution algorithms
to certain classes of functions involving exponential scales may help
shed new light on various interesting problems in real analytic geometry,
coming from Pfaffian geometry and dynamical systems. Examples of particular
interest to us are the classes of multisummable and of resurgent functions.
This workshop will survey progress made during and after our programme,
with a particular emphasis on work done by the (then) more junior
participants.